Problem: $\begin{aligned} &X = 7w^2+4w-6 \\\\ &Y = w^2-11w+13 \end{aligned}$ $X+Y=$
Solution: Since we are asked to find $X+Y$, let's substitute in the trinomial expressions that we are given for $X$ and $Y$ : $X+Y = (7w^2+4w-6)+(w^2-11w+13)$ When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${w^2}, {w},$ and the $\text{{constant}}$ term: ${{7w^2} {+4w} {-6} {+w^2} {-11w} {+13}}$ Note that since neither set of parentheses affects the order of operations or changes the values of the coefficients, we can just remove them. Also note that there is an "invisible" coefficient of $1$ in front of the term ${w^2}$. Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(7+1)w^2} + {(4-11)w} + {(-6+13)}}$ When we add the coefficients in front of each term, we get the following trinomial: ${8w^2-7w+7}$